Evaluate the Integral by Making the Given Substitution $$\int x ^ { 2 } \sqrt { x ^ { 3 } + 2 } d x , \quad u = x ^ { 3 } + 2$$

Evaluate the integral by making the given substitution.
$$\int x ^ { 2 } \sqrt { x ^ { 3 } + 2 } d x , \quad u = x ^ { 3 } + 2$$